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19 Cards in this Set
- Front
- Back
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Theorem 68
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Every triangle is cyclic.
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Corollary to Theorem 68
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The perpendicular bisectors of the sides of a triangle are concurrent.
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Theorem 69
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A quadrilateral is cyclic iff a pair of its opposite angles are supplementary.
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Theorem 70
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Every triangle has an incircle.
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Corollary to Theorem 70
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The angle bisectors of a triangle are concurrent.
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Theorem 71
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The medians of a triangle are concurrent.
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Theorem 72
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The lines containing the altitudes of a triangle are concurrent.
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Theorem 73: Ceva's Theorem
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Three cevians, AY, BZ, and CZ, of Triangle ABC are concurrent iff AX/XB x BY/YC x CZ/CA = 1.
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Construction 1
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To circumcircle a circle about a triangle.
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Construction 2
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To inscribe a circle in a triangle.
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Centroid
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The centroid of a triangle is the point in which the medians ( A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side. ) are concurrent.
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Cevian
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A cevian of a triangle is a line segment that joins a vertex of the triangle to a point on the opposite side.
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Circumcircle and Circumcenter
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See page 531
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Circumscribed Polygon
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The Circle is circumscribed about the polygon. Also see page 542
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Cyclic Polygon
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A polygon is cyclic iff there exists a circle that contains all of its vertices.
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Incircle and Incenter
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See page 542
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Inscribed Polygon
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A polygon is inscribed in a circle iff each vertex of the polygon lies on the circle. Also see page 542
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Median
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A median of a triangle is a line segment that joins a vertex to the midpoint of the opposite side.
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Orthocenter
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The orthocenter of a triangle is the point in which the lines containing its altitudes are concurrent.
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